HUNGARIAN JOURNAL OF INDUSTRIAL CHEMISTRY VESZPREM Vol. 30. pp. 199 - 206 (2002) APPLICATION OF FOURIER TRANSFORMATION FOR WASTE MINIMIZATION IN BATCH PLANTS. 1. ANALYSIS OF PRODUCTION RECIPES N. G. VAKLIEVA-BANCHEVA, E. G. SHOPOVA and B. B. IVANOV (Institute of Chemical Engineering - Bulgarian Academy of Sciences, "Acad. G. Bontchev" Street, BU03, 1113 Sofia, BULGARIA) Received: July 2J, 2002 In the present study an alternative system oriented approach for determining the environmental impact assessments is proposed. It is based on the application of Fourier transformation for presenting the discontinuous functions of waste-w mass rates as continuous ones. Using the Fourier transformation the respective environmental impact indices are presented as functions of time and the environmental impact assessments for the given pollutant and for the entire plant are obtained. The approach is used for environmental impact analysis of production recipes based on the example of curd processing. The optimal milkfat content is obtained so that the Global BOD generated in the process is minimal. The distribution of the environmental impact level into the production cycle is presented. Keywords: environmental impact assessment, Fourier transformation Introduction Aiming to meet increased environmental regulations, the problems of pollution reduction have taken a significant place in the scientific research in the last few years. The waste decreasing concept has shifted from the "end of pipe" treatment to waste minimization at the sources [1, 2]. Following this trend, a number of systematic methodologies for waste minimization have been proposed and developed during the last decade. Hilaly and Sikdar [3, 4] have introduced the concept of generic pollution balance of a process in order to develop a systematic methodology and the resulting WAR algorithm for waste minimization. By defining a pollution index of a product for a process WAR assesses the waste generation in a given process, provides options for waste reduction and carries out a systematic handling sensitivity analysis of waste minimization tasks on the target process modifications. At the same time, Linninger at al., [5] proposed another systematic approach for batch process conceptual design. According to it a synthesis of utopian process with Zero A voidable Pollution (ZAP) is carried out first. which is then followed by a guided evaluation to the process with Minimum Avoidable Pollution (MAP). The approach is implemented through a computer~aided tool BatchDesign-Kit [6]. The new development in this direction is a methodology for Minimum Environmental Impact Contact information: E-mail: vaklieva@bas.bg (MEl), developed by Pistikopoulos and others and introduced firstly for continuous processes P, 8], and further extended for batch plants [9]. The MEl methodology embeds the principles of Life Cycle Analysis within an optimization framework and involves the following steps: i) definition of a process system boundary; ii) environmental impact assessment~ and iii) incorporation of environmental impact criteria explicitly as objectives together with economics in different optimization problems. In step (ii), the environmental impact assessment is carried out using appropriately defined environmental impact indices. These indices are measures for air pollution - Critical Air Mass, CTAM (defined for continuous processes [7, 8] as [(pollutant mass rate in kg wastelh)/(standard limit value in kg waste/kg air)}), for water pollution - Critical Water Mass., CTWM , for solid wastes - Solid Mass Disposal, SMD , etc. Similar indices could be defined by using other ecological "indicators" such as BOD, COD. TSS, etc. The integral values of the defined indices over a time period H produce the environmental impact assessments: Environmental Impact for a given pollutant-w • Elw. and Global Environment wil (t) of w-polluting for one production cycle is: 1 0 for O~t~Tsil wu (t) = B;~wil for Ts 11 ~ t ~ Tsil + ~~ ' 0 for Tsu+~1 ~t~TC; when: Tsil is the starting time of task -l with regard to the cycle beginning; Bi [kg] is the batch size; and mwu [kg/kg] is the mass of the waste - w processed from the production task - l per a unit target product. Bimwil The expression [kglh] presents the waste - w r;l, mass rate. The function wu (t) depicts a cyclic discontinuous function with a period TC; into the time horizon H, as is shown on Fig.l. It is well known that each discontinuous function with a period T > 0 can be approximated with the Fourier series: a .. 'P(t) =--.!!.. + L [a1 sin(k~Pt )+ b1 cos{ktpt }1 - T ~ t ~ T, (5) 2 k=l when k is a series order. The function confessions are determined as follows: 2r a0 =-Jlf(t)dt, To (6) lit lit lit t [h] Fig. I Cyclic discontinuous function of the polluting from the routine waste source 2T ak =-J 'I'(t)sin(kqJt }lt, To 2T bk =-J 'I'(t)cos(kQJt )dt. To (7) (8) The discreet periodic function wil (t) can also be approximated with a Fourier series into the horizon H _ where the determined confessions according to (6)-(8) are: (9) [ co{ k 2 n Ts;z Il- co{ k 2n ~~ J] + B;mwil TC; TC; a(wil)k = k~z . ( k2n J . ( k2n J +sm --Tsil sm --~1 TC; TC; (10) The function. wit (t) transformed in the Fourier series into the timy horizon His 21! where - = (/J· TCi ' (12) for05:t$H The new function Fw;t (t) "wraps up" the emissions from a given routine source into a "shell" which is 201 continuous in the time horizon. It describes adequately the w-waste mass rate from a given routine source because it is presented through w-waste mass balance per a unit target product, and contains such parameters as batch size, cycle time and processing time that characterize the product - i manufacture in the plant. The function Fwu (t) allows determination of the w- waste mass rate at any moment t from H. By using functions Fwu (t) the routine sources of the waste· w which belong not only to a given product but also to a system of compatible products can be ~·wrapped up" into a common "shell" in the time horizon: where: Fw(t) = LLFwil(f), i l 'r;f/ ELi, "diE I, for 0'5t'5. H (13) Li is a number of production tasks of product - i ; and I is a number of products compatible in the horizon H. The function Fw(t) presents the w-waste mass rate in the time horizon and can be used for the determination of the respective environmental impact indices. If the pollutant- w is emitted into the air, when using Eq.(13) the respective environmental indices are expressed as a function of t. For example for air pollution they are: where: 1 CTAM w(t) =-L.LFwil(t), )-tt41 i l "'Il E Lp ViE /, for0'5.t'5.H (14~1 J-lw is the standard limit value for the pollutant· w into the air. The environmental impact indices can also be presented in accordance with the Eq.( 1) for a whole horizon H. In this case the processed w-waste mass from one routine source or from a set of routine sources belonging to one or a system of compatible products is obtained through integrating over the time horizon H: H (M wil )H == f F14.if (t)dt (15) 0 11 (M .... )H = LLf F ... 11 (t}dt. i l 0 (16} 'V l E L, 'ViE I Using (16) the environmental impact indices CTAM Hw, CTWM 11..,, SDM 11,.,., etc. at the whole horizon H are: 202 Table 1 Content of the standardized whole milk. BOD = 10 Composition 1. Water 2. Total solids milkfat lactose proteins - total casein 87% 13% content 3.6% 5% 3.25% 2.85% 1 H CTAMHw = L,L,-fFwu(t)dt (17) i l f..lw 0 It is obvious that Eq.(l7) is integrated over H Eq.(14). It is important to note that ·the Eq.( 17) has an analytical solution at H and the Fourier series at k = 1 could be used for the purposes of waste minimization problems. Using (17) the respective environmental assessments - ElHw for a pollutant -w, and for the entire process GEIH are: EI Hw = [CTAM Hw CTWM Hw SDM nwl (18) The application of the Fourier transformation, for adequate description of pollution from discreet routine sources of batch plants has been presented. By using it, the periodic discontinuous fiction of the w-pollutant mass rate from a given source is approximated with a continuous one in the time horizon. This approximation is extended to the sources that belong not only to one product but also to a system of compatible products in a given horizon. Using the Fourier transformation the respective environmental impact indices are presented as functions of time. Their integrals over the time horizon H are used for determination of the environmental impact assessments for the given pollutant and for the entire plant. Environmental Impact Analysis of Production Recipes on the Example of Curd Production The biochemical oxygen demand - BOD, is a measure of effluent strength in terms of the amount of dissolved oxygen utilized by microorganisms during the oxidation of organic components. The wastewater discharged from dairy plants contains a significant amount of proteinst milkfat, lactose and other organic matters. Some of these pollutants come as a result of dairy processing such as pasteurization, vat-processing draining etc. while the rest are due to losses of raw materialy by-product and product, for example spined and leaked milk or whey~ coagulated milk, butter, curds or cheese particles glued to unit wans. GeneraUy1 the BOD loading from dairy processing depends on the composition and the amount of processed raw materials - whole and/or skimmed milk. The biochemical oxygen demand of the milk is: Table 2 Description of the production tasks in curds processing. CYl(x)* is yield of curds by-product and xis milkfat content in skimmed milk Production Task tasks Duration Input/Output Task 1 30 min. In. Skim-milk Out. Pasteurized Skim-milk Task 2 240 min. In. Skim-milk In. Culture Out. Curds by-product Out. Whey Fractions 1 0.88 0.12 CYl(x)* 1-CYl(x) Task3 30 min. In. Curds by-product 1 Out. Curds target product 0.9 Out. Drained Whey 0.1 BODM =0.89.MF%+1.03l.MP%+0.69.ML% (20) where (MF% ), (MP%) and (ML%) are the content of the main milk components milkfat, proteins and lactose. It is accepted in the world practice [10, 11] to standardize the whole milk (Table 1) which is the base for determining the milk composition required for products manufacturing and to account BOD "processed" in different production tasks. The contribution of product losses could reach up to 80% of the common BOD load. That is why the BOD is used as a loss measure during handling and processing [10]. Taking into account that losses cannot be avoided, it is a common practice to assess their impact by using the established levels of the inherent losses. Purpose of the analysis Generally, the purpose of the environmental impact analysis of production recipes is to find the optimal conditions for product manufacturing at minimum environmental impact. It is very impqrtant to note that this analysis is carried out with regard to 1-kilogram target product processed and the particular process/unit assignment is not taken into account. Using the proposed approach, the aim of the environmental impact analysis of curd production recipe is: I. To determine the optimal milkfat content of the used skimmed milk in such a way that the Global Environmental Impact assessment- Global BOD is minimal. In the analysis both BOD "processed" in production tasks and BOD due to accounted inherent losses are considered; 2. To show the distribution of the environmental impact level into the production cycle at different operational modes. Production recipe and products content The curd is a 1owfat milk product It contains about 80% water and 20% solids- proteins (mainly casein) fat, minerals, microelements and other milk compounds. Table 3 The product compositions and calculated values of the recovery factors Composition of the curd target Values of the recovery products factors moisture % FC % CC % SC % RS RC FDM RF A 80 0.3 11.3 20 1.724 0.96 0.015 0.075 B 81.58 1.009 12.28 18.42 1.386 0.96 0.055 0.231 The curd is processed from milk skimmed in the boundaries of 0.05% ~ x ~ 1.4% (x is % of milkfat) by direct acidification with lactic acid-producing bacteria or acidifiers. The curd production is a cyclic batch process. Its flow chart and the description of the respective production tasks are presented on Fig.2 and in Table 2 [9-11]. The yield of the target product depends on the milkfat and casein content in the skim-milk. The lactose is fully passed into the whey. The Van Slyke equation for yield calculation is used [12]: where: X CY(x)= [RF.x+RC.MC%(x)]RS SC% (21) is milkfat content in the skim-milk MC%(x) casein content in the skim-milk presented as a function of milkfat content. RC, RF, RS are factors of casein, milkfat and other solids recovery from the milk; SC% is the solids content in the target product. One is accepted RC ::::: 0.96 , while RS is determined SC% as RS ~ where CC%, FC% are the CC%+FC% casein and fat content in the curd. The fat recovery factor RF is calculated by using Fat in Dry Matter factor- FDM at milkfat x = 1 % [12]: FDM and RF.(x=1%) [RF.(x=l%)+RCMC%(x=1%)}RS' FDM total fat retained in curds total solids in curds (22) For the purpose of the environmental impact analysis two types of curds - target products data are used. The first one, called Product A contains 0.3 % fat, while the second - Product B contains 1.0 % fat. The product compositions and calculated values of the above factors are presented in Table 3. Each of the above production tasks is source of pollution in curds processing due not only to the process hut also to the inherent losses associated with the by- product and target product. Each of the pollutants is characterized with the own BOD load. 203 Whey by- Drained Fig.2 Flow chart of the curd processing. Task 1 Skim-milk pasteurization. Task 2 Acidification. Task 3 Draining Waste sources and pollutant Task 1 -pasteurization. The pollutant processed in pasteurization is due to coagulated milk glued to the pasteurizer's walls. The BOD "generated" from this task depends on the mass of the pasteurized milk. The associated BOD at each kilogram processed milk is BODp = 1.5.10-3 kg 02 kg pasteurized milk Task 2- acidification. The pollution from this task results from spilled whey. It is accounted for as inherent loss. The leak is WL % = 1.6 % from the processed whey mass. The BOD load of !-kilogram acid whey is BODw =32.10-3 kgO-:. . kg acid whey Task 3- draining. The polluting from this task is due to: 1. Discharging of drained whey which remained in the curd. The amount of the waste depends on its fraction in the curd by-product (see Table 2). The BOD load of 1-kilogram acid whey is BODw =32.10-3 kg 02 . kg acid whey 2. Inherent loss of target product as a result of gluing to the drainer's walls. The leak depends on the curd fat content and is determined as CL% =0.0017.FC%, where FC % is curd fat content which for producrs A and B is 0.3% and 1,009% respectively. The BOD load of !-kilogram curd depends on the curd yield and the BOD of used skimmed milk for it manufacturing - BODc(x) = CY(x).BODM (x) kg 0~ • kg curds Consequently, the effluent from curd production will contain the three types of waste processed from its three tasks - routine sources. Environmental impact indices. Global BOD. The total amount of BOD generated in the horizon H measures the curd processing global environmental impact. It is called Global BOD. In order for it to be determined (see section l) a description of polluting from respective routine sources and their environmental impact indices could be carried out. Generally, the BOD "processed" in the sources, depends on the mHkfat content. which affects the processed materials and product and by-products yield. 204 ~ .. ; BOtxx) g- i G 1 ~ ..0.01414<. 0.0113$35 00113525 O.Oit352 0.05 0.2 0.4 0.6 0.8 X Mii:Jattontentin~ Product A ~ OllODtxl 0.01412 @- ~ 0 0.2 0.4 0.6 0.8 nos x Mikt'tltcattmtin~ ProductB 1.2 1.4 1.5 1.2 1.4 1.5 - Fig.3 The functions GBODrc (x) for products A and B To express the milkfat dependence of the environmental impact indices the production tasks mass balance is used to determine the mass of the wastes referred to 1- kilogram target product processed at each routine source - m(x)wl [kg/kg]: 0 1-CY(x) 1+-[ 0.1] -----==---0-.9-=.WL% CY(x) 0 w = 1,2,3; l = 1.2,3 0 0.1 0.9 l.CL% (23) The batch size is considered equal to 1-kilogram curd. The BOD of one kilogram pasteurized milk~ whey and curd are: [ BODP l BOD(x)w:::: BODw . , w= lt2,3 (24) BODc(x) To define the respective indices in accordance with Eq.( 17) time data are required. The duration of the time horizon is very important. Curd production is a cyclic process~ consequently the time horizon equals the duration of production cycle detennined by the Cycle Time. The cycle time depends on the chosen·operational mode. For the purpose of analysis, the two most used operational modes are discussed: J. Operation with cycles overlapping - Case A. where TC=max7; =240[min}: 2. Operation without cycles overlapping - Case B. J where TC= }:,1; =300[min]. 1•1 Other time data in [min] for tasks duration and for tasks starting time referred to the cycle beginning for both cases are: ~=[:J [210] Ts1 = 0 , l =1,2,3 (25-Case A) 240 ~=[~:]. Ts1 =[~o J l = 1,2,3 (25- Case B) 270 Using (23-25) the Environmental Impact Indices are presented as functions of the milkfat content: 3 TC BODrc(x)w = 'L,BOD(x)w J F:,1(x,t)dt (26) where l=I 0 2Bm(x),..1 1 + L 1 TC 2 k k({JT; · (1- cos(k({JT; )) + . [ cos(k({JTs1 )· l + sin(k({JTs1 )· ·sin(k({JT;) ·sin(k({Jt)+ + · (cos(k({JT; )-1)+ . [ sin(k({JTs1 )· l +cos(k({JTs1 )· ·sin(k({JT;) ·cos(k({Jt) 27r for 0 ~ t ~ TC and-= ({J TC (27) The Global BOD - (GBOD) assessing the environmental impact of the !-kilogram curd processing over one production cycle presented as a function of the milkfat content-xis: 3 GBOD(x) = LBODrc(X)w · (28) w=l Minimum of function (28) MIN GBOD(x), 0.05~1.4 (29) corresponds to the milkfat- x in skimmed milk at which the Global BOD at interval 0 ~ t ~ TC is minimal. Results: Based on the Fourier transformation the Global BOD for one production cycle is presented as continuous function of the milkfat content. The functions (28) for both products A and B are shown on Fig.3. The minimal values of GBOD for both products and corresponding optimal milkfat content - x are presented in Table 4. The yield of curd from one kilogram milk at the determined milkfat content according to Eq.(21 )is 0.248 kg for product A and 0.23 kg for product B. The values of the Impact indices calculated according (26) for the processing routine sources at the Table 4 The minimal values of GBOD for products A and B and corresponding optimal milkfat content - x Products Product A ProductB ~ GBOD [kgOz] 1.1352xlo-2 1.4084x10-2 ~ GBOO(t) 1°10-4 ~ .,2.707849·10- 6 • 0 0 so Case A ~-10-4 LI,766046·10- 4.1 r----. 1.5·10-4 ·~ l GBQI)(t) t•I0-4 I- ~ s·w-5 L6.28216•to- 6 .. 0 0 100 CaseB 100 ' x milkfat content in % ' [min] [nNn] ISO 0.858 1.052 200 240 I J 250 JOO JOO Fig.4 Distribution of the level of the biological oxygen demand for Product A processing at x = 0.858 into the production cycle for both operational modes (Case A and Case B) determined optimal milkfat content for both products are summarized in Table 5~ From the table it is seen that the BOD due to accounted inherent losses has a significant contribution to the GBOD and constitutes 21,8 % and 33,9 % for products A and B respectively. The increased contribution of Product B results from its higher fat content. Distribution of the environmental impact level into the production cycle. The distribution of the environmental impact indices in the time interval H can be presented based on Eq.(l4). Using functions (27) the distribution of the level of the biological oxygen demand for curds processing into the production cycle 0 ~ t ~ TC can be expressed at the calculated optimal values of milkfat content as: 3 3 GBODrc(X,t)w:::: LLBOD(x)w.Fw1(x,t) (30) x=0.858 W=l 1=1 or x=l.052 Results: For both operational modes Case A and Case B functions (30) are presented on Fig.4 for Product A and on Fig.5 for product B. It is obvious from both figures 205 Table 5 The values of the Impact indices according (26) for the processing routine sources at the determined optimal milkfat content Values of the Environmental impact Product Source indices [kg 0 2] Pollutant Pollutant Pollutant Curds Pasteurization Whey target product A Task 1 5.32xlo-3 x=0.858 Task2 1.495xlo-3 Task3 3.556x10-3 9.87><104 B Taskl 5.749xl0-3 x= 1.052 Task2 1.661xl0·3 Task3 3.556x10·3 3.118xlo-3 I r I I - I ,;;!.!i0089H06. 0 l____b=l:::==±===::l:==:::±::li_...J 0 100 Case A I '"""J 1!10 240 "l"I0-4 .-----.----.---.----.----.-....._., .,l.215397·I0- 4 , ·ii 2"10-4 1=----, ~ ~ GBOJl{r) ~ 1'10-4 1- r- 1 I oLo~=±!IO==~,oo====~~~====~===d~~~~ CaseB 1 !""'' 110 Fig.5 Distribution of the level of the biological oxygen demand for Product B processing at x=1.052 into the production cycle for both operational modes (Case A and Case B) that the level of the environmental impact during curdsprocessing is greatest in the first and last 30 minutes of the cycle duration. For Case A the overlapping of tasks 2 and 3 at the beginning of the time interval and this of 2 and I at its end fonns the impact level, while for Case B it is formed from task 1 in its beginning and task 3 in its end. Moreover it can be seen from both figures that the higher fat content of Product B makes the impact level of task 3 dominating compared to Product A where the impact level of task 1 is dominating. The above results could be used to look for opportunities for environmentally efficient control of batch processes. Conclusions and Comments The example above illustrates the opportunities of the proposed alternative system oriented approach for determination of environmental impact assessments. 206 Based on the application of the Fourier transformation, it adequately describes polluting from discreet routine sources. The approach is used for environmental impact analysis of the curd production recipe. The optimal milkfat content is obtained so that the Global BOD generated in the process is minimal. The distribution of the environmental impact level into the production cycle is presented. The obtained results show that: 1. The minimum value of the Global BOD is reached at different milkfat content depending on the target product fat content (x = 0.858 for Product A and x= 1.052). 2. The inherent losses have a significant contribution to the GBOD. They constitute 21,8 % and 33,9 % for products A and B. Consequently, they must be taken into account in the environmental impact assessment of dairy processing. 3. The operational mode affects the level and distribution of environmental impact into the production cycle, which is very important for -environmentally efficient control of batch processes. The environmental impact analysis of production recipes provides the optimal conditions for product manufacturing at minimum environmental impact which could be used at the scheduling and controlling levels of batch plants. The proposed system oriented approach based on the Fourier transformation application can find a number of practical applications in different engineering problems. Acknowledgement This study is conducted with the financial support of the Bulgarian National Science Fund under the Contract X- 1108/01. B CC% CL% FC% FDM H I L MC% RC RF RS SC% T TC Ts SYMBOLS batch sizes [kg]; casein content in the curd; inherent loss of curd; fat content in the curd; Fat in Dry Matter factor; time horizon [hJ ; number of products; number of production tasks; casein content in the skim-n;lilk; factors of casein recovery from the milk; factors of milkfat recovery from the milk; factors of other solids recovery from the milk; solids content in curd; production time (h1 ~ cycle time [h]; starting time of task with regard to the cycle beginning; · .WL% m inherent loss of whey; mass of waste processed from the production task per a unit target product [kg/kg] ; time [h]; X milkfat content in skim-milk. Subscripts: product; k a series order; production task; w waste. Greek the standard limit value for the pollutant. REFERENCES 1. RliTMEYER R. W.: Chern. Eng. Prog., 1991, May, 56-62 2. SMITH R. and Petela E.: TCE, 1991, 31 October, 24-25 3. HILALY A. K. and SIKDAR S. K.: J. Air Waste Manage. 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